STABILITY OF RIESZ BASES.

The Kato Theorem on similarity for sequences of projections in a Hilbert space is extended to the case when both sequences consist of nonselfadjoint projections. Passing to subspaces, this leads to stability theorems for Riesz bases of subspaces, at least one of which is finite dimensional, and for arbitrary vector Riesz bases. The following is proved as an application. If {φn}∞ n=1 is a Riesz basis and |θn| ≤ C for large n, where the constant C depends only on {φn}∞ n=1, then {φn + θnφn+1}∞ n=1 also forms a Riesz basis. [ABSTRACT FROM AUTHOR]